Numerical Integration 1

Author : Philip J. Davis,Philip Rabinowitz
Publisher : Academic Press
Page : 628 pages
File Size : 43,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483264288

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Methods of Numerical Integration by Philip J. Davis,Philip Rabinowitz Pdf

Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.

Author : W. F. Eberlein
Publisher : Unknown
Page : 18 pages
File Size : 54,5 Mb
Release : 1954
Category : Numerical integration
ISBN : UOM:39015095244052

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Numerical Integration 1 by W. F. Eberlein Pdf

Author : Gilbert Strang
Publisher : Wellesley-Cambridge Press
Page : 500 pages
File Size : 40,5 Mb
Release : 2017-09-14
Category : Mathematics
ISBN : 0980232759

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Calculus by Gilbert Strang Pdf

Gilbert Strang's clear, direct style and detailed, intensive explanations make this textbook ideal as both a course companion and for self-study. Single variable and multivariable calculus are covered in depth. Key examples of the application of calculus to areas such as physics, engineering and economics are included in order to enhance students' understanding. New to the third edition is a chapter on the 'Highlights of calculus', which accompanies the popular video lectures by the author on MIT's OpenCourseWare. These can be accessed from math.mit.edu/~gs.

Author : Gwynne Evans
Publisher : Unknown
Page : 350 pages
File Size : 46,7 Mb
Release : 1993-08-24
Category : Mathematics
ISBN : UOM:39015029997528

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Practical Numerical Integration by Gwynne Evans Pdf

Offers the quadrature user a selection of the most effective algorithms in each of the main areas of the subject. Topics range from Simpson's rule and Gaussian quadrature to recent research on irregular oscillatory and singular quadrature. A full set of test examples is given and implemented for each method discussed, demonstrating its practical limitations.

Author : Ernst Hairer,Christian Lubich,Gerhard Wanner
Publisher : Springer Science & Business Media
Page : 526 pages
File Size : 48,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662050187

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Geometric Numerical Integration by Ernst Hairer,Christian Lubich,Gerhard Wanner Pdf

This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.

Author : Sergio Blanes,Fernando Casas
Publisher : CRC Press
Page : 233 pages
File Size : 54,5 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781482263442

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A Concise Introduction to Geometric Numerical Integration by Sergio Blanes,Fernando Casas Pdf

Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.

Author : Helmut Brass,Knut Petras
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 44,7 Mb
Release : 2011-10-12
Category : Mathematics
ISBN : 9780821853610

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Quadrature Theory by Helmut Brass,Knut Petras Pdf

Every book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems. The inclusion of the word ``theory'' in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called ``co-observations,'' which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of co-observations are examined, as a detailed understanding of these is useful for solving problems in practical contexts. While quadrature theory is often viewed as a branch of numerical analysis, its influence extends much further. It has been the starting point of many far-reaching generalizations in various directions, as well as a testing ground for new ideas and concepts. The material in this book should be accessible to anyone who has taken the standard undergraduate courses in linear algebra, advanced calculus, and real analysis.

Author : Germund Dahlquist,Ake Bjorck
Publisher : SIAM
Page : 741 pages
File Size : 43,7 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780898716443

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Numerical Methods in Scientific Computing: by Germund Dahlquist,Ake Bjorck Pdf

This work addresses the increasingly important role of numerical methods in science and engineering. It combines traditional and well-developed topics with other material such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions.

Author : National Research Council (U.S.). Committee on Numerical Integration,Albert Arnold Bennett
Publisher : Unknown
Page : 118 pages
File Size : 52,7 Mb
Release : 1956
Category : Differential equations
ISBN : UOM:39015000978687

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Numerical Integration of Differential Equations by National Research Council (U.S.). Committee on Numerical Integration,Albert Arnold Bennett Pdf

Author : Christoph W. Ueberhuber
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642591181

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Numerical Computation 1 by Christoph W. Ueberhuber Pdf

This book deals with various aspects of scientific numerical computing. No at tempt was made to be complete or encyclopedic. The successful solution of a numerical problem has many facets and consequently involves different fields of computer science. Computer numerics- as opposed to computer algebra- is thus based on applied mathematics, numerical analysis and numerical computation as well as on certain areas of computer science such as computer architecture and operating systems. Applied Mathemalies I I I Numerical Analysis Analysis, Algebra I I Numerical Computation Symbolic Computation I Operating Systems Computer Hardware Each chapter begins with sample situations taken from specific fields of appli cation. Abstract and general formulations of mathematical problems are then presented. Following this abstract level, a general discussion about principles and methods for the numerical solution of mathematical problems is presented. Relevant algorithms are developed and their efficiency and the accuracy of their results is assessed. It is then explained as to how they can be obtained in the form of numerical software. The reader is presented with various ways of applying the general methods and principles to particular classes of problems and approaches to extracting practically useful solutions with appropriately chosen numerical software are developed. Potential difficulties and obstacles are examined, and ways of avoiding them are discussed. The volume and diversity of all the available numerical software is tremendous.

Author : G.N. Milstein
Publisher : Springer Science & Business Media
Page : 190 pages
File Size : 53,7 Mb
Release : 1994-11-30
Category : Computers
ISBN : 079233213X

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Numerical Integration of Stochastic Differential Equations by G.N. Milstein Pdf

This book is devoted to mean-square and weak approximations of solutions of stochastic differential equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations. Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book is of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.

Author : Michael A. Golberg
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 49,5 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489925930

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Numerical Solution of Integral Equations by Michael A. Golberg Pdf

In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.

Author : Philip J. Davis,Philip Rabinowitz
Publisher : Unknown
Page : 250 pages
File Size : 44,7 Mb
Release : 1967
Category : Numerical integration
ISBN : UOM:39015001315673

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Numerical Integration by Philip J. Davis,Philip Rabinowitz Pdf

Author : Maurizio Petrelli
Publisher : Springer Nature
Page : 229 pages
File Size : 43,5 Mb
Release : 2021-09-16
Category : Science
ISBN : 9783030780555

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Introduction to Python in Earth Science Data Analysis by Maurizio Petrelli Pdf

This textbook introduces the use of Python programming for exploring and modelling data in the field of Earth Sciences. It drives the reader from his very first steps with Python, like setting up the environment and starting writing the first lines of codes, to proficient use in visualizing, analyzing, and modelling data in the field of Earth Science. Each chapter contains explicative examples of code, and each script is commented in detail. The book is minded for very beginners in Python programming, and it can be used in teaching courses at master or PhD levels. Also, Early careers and experienced researchers who would like to start learning Python programming for the solution of geological problems will benefit the reading of the book.

Author : CK-12 Foundation
Publisher : CK-12 Foundation
Page : 603 pages
File Size : 46,6 Mb
Release : 2010-08-15
Category : Mathematics
ISBN : 9781935983019

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CK-12 Calculus by CK-12 Foundation Pdf

CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.